Equation of state and liquid-vapor equilibria of one- and two-Yukawa hard-sphere chain fluids: theory and simulation

The accuracy of several theories for the thermodynamic properties of the Yukawa hard-sphere chain fluid are studied. In particular, we consider the polymer mean spherical approximation (PMSA), the dimer version of thermodynamic perturbation theory (TPTD), and the statistical associating fluid theory for potentials of variable attractive range (SAFT-VR). Since the original version of SAFT-VR for Yukawa fluids is restricted to the case of one-Yukawa tail, we have extended SAFT-VR to treat chain fluids with two-Yukawa tails. The predictions of these theories are compared with Monte Carlo (MC) simulation data for the pressure and phase behavior of the chain fluid of different length with one- and two-Yukawa tails. We find that overall the PMSA and TPTD give more accurate predictions than SAFT-VR, and that the PMSA is slightly more accurate than TPTD.     

Discrete perturbation theory applied to Lennard-Jones and Yukawa potentials

Discrete perturbation theory (DPT) is a powerful tool to study systems interacting with potentials that are continuous but can be approximated by a piecewise continuous function composed of horizontal segments. The main goal of this work is to analyze the effect of several variables to improve the representation of continuous potentials in order to take advantage of DPT. The main DPT parameters chosen for the purpose are the starting location and size of the horizontal segments used to divide the full range of the potential and its maximum reach. We also studied the effect of having each segment aligned to the left, to the right, or centered on the continuous function. The properties selected to asses the success of this strategy are the orthobaric densities and their corresponding critical points. Critical parameters and orthobaric densities were evaluated by DPT for each of an ample set of variables and compared with their values calculated via discontinuous molecular dynamics. The best sets of DPT parameters are chosen so as to give equations of state that represent accurately the Lennard-Jones and Yukawa fluids.     

Equilibrium properties of dense hydrogen isotope gases based on the theory of simple fluids

We present a new method for the prediction of the equilibrium properties of dense gases containing hydrogen isotopes. The proposed approach combines the Feynman-Hibbs effective potential method and a deconvolution scheme introduced by Weeks et al. The resulting equations of state and the chemical potentials as functions of pressure for each of the hydrogen isotope gases depend on a single set of Lennard-Jones parameters. In addition to its simplicity, the proposed method with optimized Lennard-Jones potential parameters accurately describes the equilibrium properties of hydrogen isotope fluids in the regime of moderate temperatures and pressures. The present approach should find applications in the nonlocal density functional theory of inhomogeneous quantum fluids and should also be of particular relevance to hydrogen (clean energy) storage and to the separation of quantum isotopes by novel nanomaterials.     

Modeling the phase behavior of H2S+n-alkane binary mixtures using the SAFT-VR+D approach

A statistical associating fluid theory for potential of variable range has been recently developed to model dipolar fluids (SAFT-VR+D) [Zhao and McCabe, J. Chem. Phys. 2006, 125, 104504]. The SAFT-VR+D equation explicitly accounts for dipolar interactions and their effect on the thermodynamics and structure of a fluid by using the generalized mean spherical approximation (GMSA) to describe a reference fluid of dipolar square-well segments. In this work, we apply the SAFT-VR+D approach to real mixtures of dipolar fluids. In particular, we examine the high-pressure phase diagram of hydrogen sulfide+n-alkane binary mixtures. Hydrogen sulfide is modeled as an associating spherical molecule with four off-center sites to mimic hydrogen bonding and an embedded dipole moment (micro) to describe the polarity of H2S. The n-alkane molecules are modeled as spherical segments tangentially bonded together to form chains of length m, as in the original SAFT-VR approach. By using simple Lorentz-Berthelot combining rules, the theoretical predictions from the SAFT-VR+D equation are found to be in excellent overall agreement with experimental data. In particular, the theory is able to accurately describe the different types of phase behavior observed for these mixtures as the molecular weight of the alkane is varied: type III phase behavior, according to the scheme of classification by Scott and Konynenburg, for the H2S+methane system, type IIA (with the presence of azeotropy) for the H2S+ethane and+propane mixtures; and type I phase behavior for mixtures of H2S and longer n-alkanes up to n-decane. The theory is also able to predict in a qualitative manner the solubility of hydrogen sulfide in heavy n-alkanes.     

Dynamical simulation of dipolar Janus colloids: Equilibrium structure and thermodynamics

The static microstructures and thermodynamics of a colloidal dispersion of dipolar Janus (DJ) particles-that is, dipolar spheres in which each hemisphere is specified by a different charge interaction-have been investigated through simulation. DJ particles are modeled at a high level of detail with pairwise potentials represented as a sum of a spherically symmetric soft repulsion and an orientation-dependent electrostatic component using continuous potentials. The latter is important because it allows for the use of conventional molecular dynamics simulations, and is in contrast to the patch model and dipolar hard sphere model, which are discontinuous and therefore do not. The electrostatics are represented through a rigorous pointwise (PW) covering of two different hemispheres filled by points of corresponding charge. An isotropic coarse-graining (CG) of the PW models serves as a limit of the structure wherein the orientations of the DJ particles can be pairwise averaged. Over the range of volume fractions and DJ charge densities studied-consistent with reversible structures absent of long-range correlations-the CG model agrees well with the PW model with respect to equilibrium structure (isotropic pair correlation) and ensemble free energy. Time-dependent relaxation simulations of the PW model suggest that chain structures are not expected in liquid phases in contrast to that which has been observed for point dipole models of simple polar fluids.     

Application of a renormalization-group treatment to the statistical associating fluid theory for potentials of variable range (SAFT-VR)

An accurate prediction of phase behavior at conditions far and close to criticality cannot be accomplished by mean-field based theories that do not incorporate long-range density fluctuations. A treatment based on renormalization-group (RG) theory as developed by White and co-workers has proven to be very successful in improving the predictions of the critical region with different equations of state. The basis of the method is an iterative procedure to account for contributions to the free energy of density fluctuations of increasing wavelengths. The RG method has been combined with a number of versions of the statistical associating fluid theory (SAFT), by implementing White's earliest ideas with the improvements of Prausnitz and co-workers. Typically, this treatment involves two adjustable parameters: a cutoff wavelength L for density fluctuations and an average gradient of the wavelet function Φ. In this work, the SAFT-VR (variable range) equation of state is extended with a similar crossover treatment which, however, follows closely the most recent improvements introduced by White. The interpretation of White's latter developments allows us to establish a straightforward method which enables Φ to be evaluated; only the cutoff wavelength L then needs to be adjusted. The approach used here begins with an initial free energy incorporating only contributions from short-wavelength fluctuations, which are treated locally. The contribution from long-wavelength fluctuations is incorporated through an iterative procedure based on attractive interactions which incorporate the structure of the fluid following the ideas of perturbation theories and using a mapping that allows integration of the radial distribution function. Good agreement close and far from the critical region is obtained using a unique fitted parameter L that can be easily related to the range of the potential. In this way the thermodynamic properties of a square-well (SW) fluid are given by the same number of independent intermolecular model parameters as in the classical equation. Far from the critical region the approach provides the correct limiting behavior reducing to the classical equation (SAFT-VR). In the critical region the β critical exponent is calculated and is found to take values close to the universal value. In SAFT-VR the free energy of an associating chain fluid is obtained following the thermodynamic perturbation theory of Wertheim from the knowledge of the free energy and radial distribution function of a reference monomer fluid. By determining L for SW fluids of varying well width a unique equation of state is obtained for chain and associating systems without further adjustment of critical parameters. We use computer simulation data of the phase behavior of chain and associating SW fluids to test the accuracy of the new equation.     

Structural properties of a model system with effective interparticle interaction potential applicable in modeling of complex fluids

We report grand canonical ensemble Monte Carlo (MC) simulation and theoretical studies of the structural properties of a model system described by an effective interparticle interaction potential, which incorporates basic interaction terms used in modeling of various complex fluids composed of mesoscopic particles dispersed in a solvent bath. The MC results for the bulk radial distribution function are employed to test the validity of the hard-sphere bridge function in combination with a modified hypernetted chain approximation (MHNC) in closing the Ornstein-Zernike (OZ) integral equation, while the MC data for the density profiles in different inhomogeneous environments are used to assess the validity of the third-order+second-order perturbation density functional theory (DFT). We found satisfactory agreement between the results predicted by the pure theories and simulation data, which classifies the proposed theoretical approaches as convenient tools for the investigation of complex fluids. The present investigation indicates that the bridge function approximation and density functional approximation, which are traditionally used for the study of neutral atomic fluids, also perform well for complex fluids only on condition that the underlying effective potentials include a highly repulsive core as an ingredient.     

Statistical mechanical theory for discotic liquid crystals Discotic nematic-isotropic transition properties

A statistical mechanical theory is applied to study the equilibrium properties of discotic nematic liquid crystals. We report the calculation of thermodynamic properties for a model system composed of molecules interacting through angle-dependent pair potentials which can be broken up into rapidly varying short-ranged repulsions and weak long-range attractions. The repulsive interaction is represented by a repulsion between hard oblate ellipsoids of revolution and is a short-range, rapidly-varying, potential. The influence of attractive potentials, represented by dispersion and quadrupole interactions on a variety of thermodynamic properties is analysed. It is found that the thermodynamic properties for the discotic nematic-isotropic transition are highly sensitive to the form of effective one-body orientational perturbation potential. The discontinuity in the transition properties is more pronounced in the case of quadrupole interaction than for anisotropic dispersion interaction. A remarkable symmetry in the transition properties between prolate ellipsoids (ordinary nematic) and oblate ellipsoids (discotic nematic) is observed.     

Resummed thermodynamic perturbation theory for central force associating potential. Multi-patch models

A resummed thermodynamic perturbation theory for associating fluids with multiply bondable central force associating potential is extended for the fluid with multiple number of multiply bondable associating sites. We consider a multi-patch hard-sphere model for associating fluids. The model is represented by the hard-sphere fluid system with several spherical attractive patches on the surface of each hard sphere. Resummation is carried out to account for blocking effects, i.e., when the bonding of a particle restricts (blocks) its ability to bond with other particles. Closed form analytical expressions for thermodynamical properties (Helmholtz free energy, pressure, internal energy, and chemical potential) of the models with arbitrary number of doubly bondable patches at all degrees of the blockage are presented. In the limiting case of total blockage, when the patches become only singly bondable, our theory reduces to Wertheim's thermodynamic perturbation theory (TPT) for polymerizing fluids. To validate the accuracy of the theory we compare to exact values, for the thermodynamical properties of the system, as determined by Monte Carlo computer simulations. In addition we compare the fraction of multiply bonded particles at different values of the density and temperature. In general, predictions of the present theory are in good agreement with values for the model calculated using Monte Carlo simulations, i.e., the accuracy of our theory in the case of the models with multiply bondable sites is similar to that of Wertheim's TPT in the case of the models with singly bondable sites.     

Elucidating the role of many-body forces in liquid water. I. Simulations of water clusters on the VRT(ASP-W) potential surfaces

We test two new potentials for water, fit to vibration-rotation tunneling (VRT) data by employing diffusion quantum Monte Carlo simulations to calculate the vibrational ground-state properties of water clusters. These potentials, VRT(ASP-W)II and VRT(ASP-W)III, are fits of the highly detailed ASP-W (anisotropic site potential with Woermer dispersion) ab initio potential to (D(2)O)(2) microwave and far-infrared data, and along with the SAPT5s (five-site symmetry adapted perturbation theory) potentials, are the most accurate water dimer potential surfaces in the literature. The results from VRT(ASP-W)II and III are compared to those from the original ASP-W potential, the SAPT5s family of potentials, and several bulk water potentials. Only VRT(ASP-W)III and the spectroscopically "tuned" SAPT5st (with N-body induction included) accurately reproduce the vibrational ground-state structures of water clusters up to the hexamer. Finally, the importance of many-body induction and three-body dispersion are examined, and it is shown that the latter can have significant effects on water cluster properties despite its small magnitude.     

Computation of the pair correlation function of a repulsive finite-intercept hard-core simple fluid

We consider a range of integral equation theories for a simple fluid with a pair potential of the type that arises for fused-hard-sphere molecular fluids in the RAM perturbation theory. The potential is of finite range with a finite intercept at contact, and is everywhere repulsive. Results based on a corrected form of the hypernetted chain theory are excellent and are superior to all others.     

Second-order post-Hartree-Fock perturbation theory for the electron current

Based on the super-fermion representation of quantum kinetic equations we develop nonequilibrium, post-Hartree-Fock many-body perturbation theory for the current through a region of interacting electrons. We apply the theory to out of equilibrium Anderson model and discuss practical implementation of the approach. Our calculations show that nonequilibrium electronic correlations may produce significant quantitative and qualitative corrections to mean-field electronic transport properties.     

Computer simulation of colloidal dispersions

This paper discusses recent applications of statistical mechanics to dispersions with particular emphasis on the computer simulation of the dynamic properties.Fundamental to any computation on a colloidal dispersion is the knowledge of the potential of mean force for at least a pair of suspended particles. At low-to-moderate particle concentrations for stable dispersions, statistical mechanical calculations based on the normal DLVO pair potential produce reasonable agreement with experiment for a number of equilibrium properties of simple latex dispersions. This phenomenon indicates that under these conditions the DLVO pair potential is a reasonable effective pair potential. However, recent Monte Carlo simulations and experimental measurements with liquids of spherical molecules suggest that the force between a pair of dispersed particles at very small separation may differ significantly from that predicted by DLVO theory.The computation of dynamic properties of dispersions involves problems not encountered in the above equilibrium calculations. In particular, one must include the effects of indirect hydrodynamic as well as direct interactions among the particles. This computation may be easily accomplished at moderately low particle concentrations and the results of such calculations are able to give a very detailed analysis of the results of Photon Correlation Spectroscopy measurements on ion exchanged polystyrene latex suspensions at low concentration. These computations also, once again, emphasize the usefulness of DLVO pair potentials as effective pair potentials for systems of strongly interacting particles.     

Transferable step potentials for perfluorinated hydrocarbons

The step potential equilibria and discontinuous molecular dynamics (SPEADMD) model is adapted for characterizing the interaction potentials of perfluorocarbons and their mixtures with n-alkanes. We seek to explain the peculiar behavior of these systems, especially with regard to the unfavorable mixing behavior. The methodology is based on discontinuous molecular dynamics (DMD) and second order thermodynamic perturbation theory (TPT). DMD simulation is applied to the repulsive part of the potential. The effects of disperse attractions and hydrogen bonding are treated by TPT, discretizing the attractive potential into four distinct wells of variable depth. This approach accelerates the molecular simulations in general and the parameterization of the transferable potentials in particular. C₃–C₈ straight chain perfluorocarbons are characterized along with perfluorobenzene, perfluorocyclobutane, and heptafluoropropane applying explicit atom models for all fluorine atoms. Each compound is simulated at 21 densities. Interpolation with density combines with TPT to give a complete equation of state. The depths of the attractive wells are optimized by iterating on their values until the vapor pressures computed by the resulting equation of state provide the minimum deviation from experimental data.     

Thermodynamic and structural properties of confined discrete-potential fluids

The thermodynamic and structural behaviors of confined discrete-potential fluids are analyzed by computer simulations, studying in a systematic way the effects observed by varying the density, temperature, and parameters of the potentials that characterize the molecule-molecule interactions. The Gibbs ensemble simulation technique for confined fluids [A. Z. Panagiotopoulos, Mol. Phys. 62, 701 (1987)] is applied to a fluid confined between two parallel hard walls. Two different systems have been considered, both formed by spherical particles that differ by the interparticle pair potential: a square well plus square shoulder or a square shoulder plus square well interaction. These model interactions can describe in an effective way pair potentials of real molecular and colloidal systems. Results are compared with the simpler reference systems of square-shoulder and square-well fluids, both under confinement. From the adsorption characterization through the use of density profiles, it is possible to obtain specific values of the interparticle potential parameters that result in a positive to negative adsorption transition.